Alice and Bob choose digits from a number with 2018 digits, different mod3
Source: 49th Austrian Mathematical Olympiad National Competition (Final Round) 28th April 2018 p3
May 25, 2019
combinatoricsgamenumber theorydecimal representationDigits
Problem Statement
Alice and Bob determine a number with digits in the decimal system by choosing digits from left to right. Alice starts and then they each choose a digit in turn. They have to observe the rule that each digit must differ from the previously chosen digit modulo . Since Bob will make the last move, he bets that he can make sure that the final number is divisible by .
Can Alice avoid that?(Proposed by Richard Henner)